She "passed away peacefully last night at Kensington Palace, surrounded by her family", a statement said on Friday, with the flag on Buckingham Palace now lowered to half mast.
The duchess, Katharine, was the oldest member of the Royal Family, married to Prince Edward, the Duke of Kent, a first cousin of the late Queen Elizabeth II.
She will be remembered as a familiar figure at the Wimbledon tennis championships, where she handed over trophies - and consoled those who had lost, famously including a tearful Jana Novotna in 1993.
The duchess was also a great music lover - supporting music charities and teaching music in a Hull primary school, where pupils knew nothing of her royal identity, and where she was known as "Mrs Kent".
Perhaps the most familiar images of the duchess are from her appearances at Wimbledon, where she was regularly seen watching the tennis and stepping on to the court to give out prizes.